William K. answered • 07/05/19
Stats/Econ/Math, PhD with 10+ yrs of teaching experience, USC
For the first two questions, need to use the z-table or the standard Normal distribution table.
Remember that the z-table values represent area to the left of the z-score.
1. right-tailed, alpha=.01
This is where all the probability is to the right of some z-score, and that probability has to be 0.01.
Because the z-table only reads from the left, right area of 0.01 is equivalent to left area of 0.99.
Hence, find the area that is closest to 0.99 or 0.9900 (most z-tables are 4 decimal places) or when the values cross over 0.9900. The values are 0.9898 and 0.9901.
Then look at the row for the first-decimal and then the columns for the second-decimal of the z-score.
The z-score corresponding to area of 0.9898 is 2.32, and the z-score corresponding to the area of 0.9901 is 2.33.
As a rule of thumb, choose the bigger (absolute) z-score.
Thus, critical z-score is 2.33.
2. two-tailed, z=-0.33
Directly from the z-table, the area to the left of z=-0.33 is 0.3707.
But this is two-tailed or double-sided, hence double the area to get the final p-value.
p-value=0.7414
For the third question, to get the exact value, we'd need something more than the t-table or the student-t distribution table.
The t-table specifies critical values, and not areas (like the z-table), based on the level of alpha and degrees of freedom.
3. left-tailed, t=-1.48
n=41, thus degrees of freedom is 40.
On the row with df=40, I look for where the (absolute) t=1.48 would fall, which is between 1.303 and 1.684.
The columns for a single-tail or one-tail would indicate that it's between alpha level of 0.05 (1.684) and 0.10 (1.303).
The p-value is thus between 0.05 and 0.10.
